Absolute stability analysis for a class of Takagi-Sugeno fuzzy control systems. (English) Zbl 1167.93365

Summary: This article presents absolute stability conditions for a particular class of Takagi-Sugeno fuzzy control systems. Initially, a Takagi-Sugeno fuzzy control system is transformed into a multivariable Lur’e type system. A simple algorithm for checking the absolute stability of this system is then proposed. Since the key of the proposed algorithm is to solve algebraic Riccati equations, software packages such as MATLAB provides a simple means to check the conditions. The proposed approach does not limit the methods of fuzzification and defuzzification. This article presents several analytical examples to verify the simplicity and efficiency of the proposed approach.


93C42 Fuzzy control/observation systems
93D09 Robust stability
93C35 Multivariable systems, multidimensional control systems


Full Text: DOI


[1] DOI: 10.1016/0165-0114(94)00325-2 · Zbl 0852.93049
[2] DOI: 10.1016/0165-0114(93)90152-8 · Zbl 0792.93079
[3] DOI: 10.1109/TFUZZ.2003.819833 · Zbl 05452546
[4] DOI: 10.1016/S0165-0114(96)00087-5 · Zbl 0925.93515
[5] Khalil HK, Nonlinear Systems,, 2. ed. (1996)
[6] DOI: 10.1109/91.324804
[7] DOI: 10.1016/S0020-7373(75)80002-2 · Zbl 0301.68076
[8] DOI: 10.1016/0165-0114(91)90110-C · Zbl 0741.93052
[9] DOI: 10.1109/TFUZZ.1993.390281
[10] Takagi T, IEEE Trans. Syst. Man Cybern. 15 pp 116– (1985) · Zbl 0576.93021
[11] DOI: 10.1109/91.481952
[12] DOI: 10.1109/91.481840
[13] DOI: 10.1109/91.277961
[14] Tufillaro NB, An Experimental Approach to Nonlinear Dynamics and Chaos (1992)
[15] DOI: 10.1109/91.660813
[16] DOI: 10.1109/91.481841
[17] DOI: 10.1109/41.679009
[18] DOI: 10.1016/0005-1098(93)90146-K · Zbl 0772.93050
[19] DOI: 10.1016/0005-1098(94)90213-5 · Zbl 0800.93711
[20] DOI: 10.1016/0165-0114(94)90142-2 · Zbl 0845.93053
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